Robust Estimation of Curvature along Digital Contours with Global Optimization

Abstract

Abstract. In this paper we introduce a new curvature estimator based on global optimisation. This method called Global Min-Curvature exploits the geometric properties of digital contours by using local bounds on tangent directions defined by the maximal digital straight segments. The estimator is adapted to noisy contours by replacing maximal segments with maximal blurred digital straight segments. Experimentations on perfect and damaged digital contours are performed and in both cases, comparisons with other existing methods are presented.

Discrete Contour Extraction from Reference Curvature Function

“…Note that a parameter ν permits to control the sensibility to noise. More details about the GMC estimator are presented in [1].…”

“…As in the smooth case, the GMC estimator always shows more precision and stability than the NDC estimator. Details and comparisons can be found in previous work [1].…”

“…The curvature will there guide the segmentation process. Our approach is based on the Global Min-Curvature (GMC) estimator introduced in [1] and is using the shortest path algorithm defined on the live-wire method. The main advantage of the GMC estimator is its noise robustness and the stability which allows to extract directly geometric information as for example local maxima/minima curvature points.…”

Comparison of Discrete Curvature Estimators and Application to Corner Detection

“…By this way, the estimation of osculating circles had a better behavior on noisy contours and was also meaningful for a non connected (but ordered) set of points. Then a second approach, proposed by Kerautret and Lachaud [2], suggests to minimize curvature while satisfying geometric constraints derived from tangent directions computed on the discrete contour. The robustness to noise of this approach was given also by blurred segments but used in a different manner.…”

“…Several curvature estimators along digital contours were proposed in recent works [1][2][3]. These estimators are adapted to non perfect digitization process and can process noisy contours.…”